Problem 13 - Chemistry Principles and Practice

Question

Assign the oxidation numbers of all atoms in the following compounds. (a) \(\mathrm{ZrO}_{2}\) (b) \(\mathrm{FeO}\) (c) \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\)

Step-by-Step Solution

Answer

(a) Zr: +4, O: -2; (b) Fe: +2, O: -2; (c) Ca: +2, N: +5, O: -2.

Step 1: Determine the Rules for Oxidation Numbers

To assign oxidation numbers, we follow a set of rules: (1) Free elements have an oxidation number of 0. (2) For a monoatomic ion, the oxidation number is the same as its charge. (3) Oxygen usually has an oxidation number of -2, except in peroxides. (4) The sum of the oxidation numbers in a compound must equal the total charge of the compound.

Step 2: Assign Oxidation Numbers in ZrO2

In \mathrm{ZrO}_{2}\, \( \text{O} \) has an oxidation number of \(-2\). There are two \( \text{O} \) atoms, contributing \(-4\) overall. Zirconium \( \text{Zr} \) must balance this out to zero, so \( \text{Zr} \) has an oxidation number of \(+4\). Thus, \( \text{O} : -2\) and \( \text{Zr} : +4\).

Step 3: Assign Oxidation Numbers in FeO

In \mathrm{FeO}\, oxygen \( \text{O} \) has an oxidation number of \(-2\). Since the compound is neutral, the iron \( \text{Fe} \) must balance this to zero, so \( \text{Fe} \) has an oxidation number of \(+2\). Thus, \( \text{O} : -2\) and \( \text{Fe} : +2\).

Step 4: Assign Oxidation Numbers in Ca(NO3)2

In \(\text{Ca(NO}_{3})_{2} \), \( \text{Ca} \) is in group 2 and has an oxidation number of \(+2\). The nitrate ion \( \text{NO}_{3}^{-} \) must sum to \(-1\). \( \text{O} \) is \(-2\) and there are three \( \text{O} \) atoms, giving \(-6\). This means \( \text{N} \) must be \(+5\) to result in \(-1\) for \( \text{NO}_{3}^{-} \). Thus, \( \text{Ca} : +2\), \( \text{N} : +5\), and \( \text{O} : -2\).

Key Concepts

Oxidation Number Rules

Understanding the rules for assigning oxidation numbers is key to solving chemical equations. Here are the basic guidelines you need:

• Free elements, like \(\mathrm{O}_2\) or \(\mathrm{N}_2\), have oxidation numbers of zero. This rule applies because no electrons are gained or lost.
• For a monoatomic ion, the oxidation number equals the ion's charge. For example, \(\text{Na}^{+}\) has an oxidation number of \(+1\), and \(\text{Cl}^{-}\) has \(-1\).
• Oxygen generally has an oxidation number of \-2\, but exceptions include molecules like peroxides (e.g., \(\mathrm{H}_2\mathrm{O}_2\)) where oxygen is \-1\.
• The sum of oxidation numbers for all atoms in a compound or ion must equal the compound's total charge. This ensures charge neutrality.

These rules form the basis for understanding how elements interact in chemical reactions. When you familiarize yourself with these concepts, the assignment of oxidation numbers becomes much more intuitive and logical.

Chemical Compounds

Chemical compounds are substances formed by the chemical combination of two or more different elements. Each element in a compound plays a role in its properties and behavior in reactions. To figure out oxidation numbers, consider the types of bonding and arrangements in compounds:

• Compounds like \(\mathrm{ZrO}_2\) are composed of zinc and oxygen. In such metal-oxide compounds, oxygen often takes its common oxidation state of \-2\, setting a standard for other elements to balance.
• In ionic compounds like \(\mathrm{FeO}\), iron balances the charge of oxygen since the entire compound is neutral. Thus, understanding compound neutrality helps guide oxidation assignments.
• Complex ions, such as those in \(\mathrm{Ca(NO}_3)_2\), may contain polyatomic ions like \(\mathrm{NO}_3^{-}\). Each polyatomic ion has an overall charge that must be accounted for when distributing oxidation states within the ion.

Through these principles, chemists can decipher detailed aspects of each element's behavior within the broader structure of the compound. This understanding also helps predict reactions and molecular interactions.

Step by Step Solution

Now, let's delve into practical applications of assigning oxidation numbers step by step. Practicing these methods helps reinforce your understanding.**Example 1: Analyzing \(\mathrm{ZrO}_2\)**- Oxygen is almost always \-2\. With two oxygen atoms, their overall contribution is \-4\.- Since \(\mathrm{ZrO}_2\) is neutral, zirconium must counterbalance the \-4\ from oxygen. So zirconium takes an oxidation number of \(+4\).- Thus, oxidation numbers are: \(\text{O} : -2\), \(\text{Zr} : +4\).**Example 2: Understanding \(\mathrm{FeO}\)**- Oxygen once again shows \-2\.- Iron (being the only other element) must balance this for a neutral compound. Hence, iron assumes an oxidation number of \(+2\).- Therefore, numbers are: \(\text{O} : -2\), \(\text{Fe} : +2\).**Example 3: Breaking down \(\mathrm{Ca(NO}_3)_2\)**- Calcium, a group 2 metal, possesses a clear oxidation number of \(+2\).- Nitrate \(\mathrm{NO}_3^{-}\) collectively holds a charge of \-1\, with oxygen assigned \-2\.- Each nitrate ion necessitates nitrogen to balance to \(+5\) (given \-6\ from three oxygens), resulting in the ion's \-1\.- Overall oxidation numbers in the compound become: \(\text{Ca} : +2\), \(\text{N} : +5\), \(\text{O} : -2\).By following these analyses, one can correctly assign oxidation numbers, supporting greater comprehension in overall chemical reactivity.